Winger Srnic, who joined Cukaricki from Partizan's bitter arch rivals Red Star in 2013, beat two markers and side-footed the ball past keeper Zivko Zivkovic in what was probably his last game for the club.
"I will remember this goal for the rest of my life," Srnic told Arenasport television.
"It's a pity it didn't come in a Red Star shirt against Partizan in a cup final but I love Cukaricki too with all my heart. It is a wonderful farewell because it's time for me to move on."
Cukaricki dominated the first half as captain Igor Matic forced a good save from Zivkovic with a lone-range effort and striker Nikola Stojiljkovic hit the post before Srnic struck in the 39th minute.
Partizan, who secured their 26th league title earlier this month, twice came close in the dying minutes.
Midfielder Darko Brasanac headed wide with the goal at his mercy and forward Stefan Babovic then missed a stoppage time chance when his overhead kick sailed just wide. (Writing by Zoran Milosavljevic; Editing by Justin Palmer)